Common fuses are blown out at a predetermined voltage or more to interrupt current. On the contrary, anti-fuse elements have been proposed which are short-circuited at a predetermined voltage or more to cause a current to flow.
For example, Patent Document 1 discloses a structure as shown in a cross-sectional view of FIG. 5. An insulation layer 108 is made of an insulation material (for example, an SiO2), and the insulation layer 108 is formed continuously so as to step over a gap 103 between wiring patterns 102a, 102t in contact with the both wiring patters 102s, 102t formed on a substrate 101. Lead terminals 104, 105 of an LED (light-emitting diode) 106 are connected to the wiring patterns 102s, 102t with the use of solders 104a, 105a. 
In a normal state, a current flows in the forward direction of the LED 106. For example, a current flows from one wiring pattern 102s, through the solder 105a, the lead terminal 105, the LED 106, the lead terminal 104, and the solder 104a, to the other wiring pattern 102t. 
However, in an open state (defective open) with no current flowing through the LED 106 due to a defective, a failure, or the like of the LED 106, the voltage applied between the wiring patterns 102s and 102t causes the insulation layer 108 to undergo insulation breakdown, and a current flows from one wiring pattern 102s through the insulation layer 108 to the other wiring pattern 102t. 
The anti-fuse element which has this configuration is used so that even if some of LEDs 111A, 111B, . . . , 111n connected in series with each other break down, the other LEDs are kept lighting-up, for example, as shown in the electrical circuit diagram of FIG. 6. In this case, anti-fuse elements 112A, 112B, . . . 112n are used in parallel connection with each of LEDs 111A, 111B, . . . , 111n connected in series with each other. In the case of defective open with no current flowing through some LEDs (for example, 111A), while the anti-fuse elements (for example, 112A) connected in parallel with the LEDs are short-circuited, a current flows around the anti-fuse elements (for example, 112A) to cause a current to flow through the other LEDs, and the other LEDs thus continue to light up.
Assuming that n LEDs are connected in series with each other and that the voltage value of the voltage drop in the forward direction of the LEDs is denoted by Vf, when the LED is brought into defective open, a voltage of approximately Vf×n is applied across the n LEDs connected in series with each other to cause the anti-fuse element to undergo insulation breakdown to be short-circuited, and thereby cause the other LEDs to light up.
FIG. 7 is a graph showing a relationship between the breakdown voltage of an anti-fuse element and a current through the anti-fuse element. In the conventional anti-fuse element as in the case of FIG. 7, insulation breakdown is started when the voltage (the applied voltage in FIG. 7) applied to the anti-fuse element is greater than the breakdown voltage (50 V).
Patent Document 1: Japanese Patent Application Laid-Open No. 2007-324355